If we want to specify the equation of a plane that goes through 3 different points we have the following determinant: $$\begin{vmatrix}x-a1&y-a2&z-a3\\b1-a1&b2-a2&b3-a3\\c1-a1&c2-a2&c3-a3 \end{vmatrix}=0$$ which comes from the mixed product of the vectors. But we can also use the following determinant: $$\begin{vmatrix}x&y&z&1\\a1&a2&a3&1\\b1&b2&b3&1\\c1&c2&c3&1 \end{vmatrix}=0$$ How can we go from the first equation to the second one?
2026-03-24 20:36:55.1774384615
Analytic equation of plane
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